Question

write a simplified expression that is equivalent to ((x + 1)(4x^2 - 5x + 3))

Explanation:

Step1: Apply distributive property (FOIL for polynomials)

Multiply \(x\) by each term in \(4x^{2}-5x + 3\) and then \(1\) by each term in \(4x^{2}-5x + 3\).
\(x(4x^{2}-5x + 3)+1(4x^{2}-5x + 3)\)
\(=4x^{3}-5x^{2}+3x + 4x^{2}-5x + 3\)

Step2: Combine like terms

Combine the \(x^{2}\) terms and the \(x\) terms.
For \(x^{2}\) terms: \(-5x^{2}+4x^{2}=-x^{2}\)
For \(x\) terms: \(3x-5x=-2x\)
So the expression becomes \(4x^{3}-x^{2}-2x + 3\)

Answer:

\(4x^{3}-x^{2}-2x + 3\)